Partitioning cryptanalysis

In cryptography, partitioning cryptanalysis is a form of cryptanalysis for block ciphers. Developed by Carlo Harpes in 1995, the attack is a generalization of linear cryptanalysis. Harpes originally replaced the bit sums (affine transformations) of linear cryptanalysis with more general balanced Boolean functions. He demonstrated a toy cipher that exhibits resistance against ordinary linear cryptanalysis but is susceptible to this sort of partitioning cryptanalysis. In its full generality, partitioning cryptanalysis works by dividing the sets of possible plaintexts and ciphertexts into efficiently-computable partitions such that the distribution of ciphertexts is significantly non-uniform when the plaintexts are chosen uniformly from a given block of the partition. Partitioning cryptanalysis has been shown to be more effective than linear cryptanalysis against variants of DES and CRYPTON. A specific partitioning attack called mod n cryptanalysis uses the congruence classes modulo some integer for partitions.

References

Carlo Harpes, Gerard G. Kramer, James L. Massey (May 1995). A Generalization of Linear Cryptanalysis and the Applicability of Matsui's Piling-up Lemma (PDF/PostScript). Advances in Cryptology — Eurocrypt '95. Saint-Malo: Springer-Verlag. pp. 24–38. Retrieved 9 September 2007.
Thomas Jakobsen (1995). "Security Against Generalized Linear Cryptanalysis and Partitioning Cryptanalysis" (PDF/PostScript). Retrieved 9 September 2007.
T. Jakobsen; C. Harpes (1996). Bounds On Non-Uniformity Measures For Generalized Linear Cryptanalysis And Partitioning Cryptanalysis (PDF/PostScript). Pragocrypt '96. Prague: Czech Technical University Publishing House. pp. 467–479. Retrieved 9 September 2007.
C. Harpes; J. Massey (January 1997). Partitioning Cryptanalysis (PDF/PostScript). 4th International Workshop in Fast Software Encryption (FSE '97). Haifa: Springer-Verlag. pp. 13–27. Retrieved 9 September 2007.
Marine Minier, Henri Gilbert (April 2000). Stochastic Cryptanalysis of Crypton (PDF). 7th International Workshop in Fast Software Encryption (FSE 2000). New York City: Springer-Verlag. pp. 121–133. Retrieved 10 September 2007.
Thomas Baignères, Pascal Junod, Serge Vaudenay (December 2004). How Far Can We Go Beyond Linear Cryptanalysis? (PDF). Advances in Cryptology — ASIACRYPT 2004. Jeju Island: Springer-Verlag. pp. 432–450. Retrieved 9 September 2007.
Gaëtan Leurent (October 2015). Differential and Linear Cryptanalysis of ARX with Partitioning (PDF). Cryptology ePrint Archive. Retrieved 10 October 2015.

Block ciphers (security summary)

Common algorithms	AES Blowfish DES (Internal Mechanics, Triple DES) Serpent Twofish

Less common algorithms	Camellia CAST-128 IDEA RC2 RC5 RC6 SEED ARIA Skipjack TEA XTEA

Other algorithms	3-Way Akelarre Anubis BaseKing BassOmatic BATON BEAR and LION CAST-256 Chiasmus CIKS-1 CIPHERUNICORN-A CIPHERUNICORN-E CLEFIA CMEA Cobra COCONUT98 Crab Cryptomeria/C2 CRYPTON CS-Cipher DEAL DES-X DFC E2 FEAL FEA-M FROG G-DES GOST Grand Cru Hasty Pudding cipher Hierocrypt ICE IDEA NXT Intel Cascade Cipher Iraqi KASUMI KeeLoq KHAZAD Khufu and Khafre KN-Cipher Kuznyechik Ladder-DES Libelle LOKI (97, 89/91) Lucifer M6 M8 MacGuffin Madryga MAGENTA MARS Mercy MESH MISTY1 MMB MULTI2 MultiSwap New Data Seal NewDES Nimbus NOEKEON NUSH PRESENT Prince Q RC6 REDOC Red Pike S-1 SAFER SAVILLE SC2000 SHACAL SHARK Simon SM4 Speck Spectr-H64 Square SXAL/MBAL Threefish Treyfer UES Xenon xmx XXTEA Zodiac

Design	Feistel network Key schedule Lai-Massey scheme Product cipher S-box P-box SPN Avalanche effect Block size Key size Key whitening (Whitening transformation)

Attack (cryptanalysis)	Brute-force (EFF DES cracker) MITM (Biclique attack, 3-subset MITM attack) Linear (Piling-up lemma) Differential (Impossible Truncated Higher-order) Differential-linear Distinguishing (Known-key) Integral/Square Boomerang Mod n Related-key Slide Rotational Timing XSL Interpolation Partitioning Davies' Rebound Weak key Tau Chi-square Time/memory/data tradeoff

Standardization	AES process CRYPTREC NESSIE

Utilization	Initialization vector Mode of operation Padding

Cryptography

History of cryptography Cryptanalysis Outline of cryptography

Symmetric-key algorithm Block cipher Stream cipher Public-key cryptography Cryptographic hash function Message authentication code Random numbers Steganography

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